Graphics Reference
In-Depth Information
It should not be a surprise that the same process also works with vectors, and we can write
w
=
1
−
u
+
v
0
1
(2.27)
Figure 2.37 illustrates values of
w
for different values of .
λ
=
0
1
4
λ
=
2
λ
=
3
4
λ
=
w
0
w
0.25
u
λ
=
1
w
0.5
w
0.75
w
1
v
Figure 2.37.
In the following chapters we will employ Eq. (2.27) to identify points that lie on a line determined
by two vectors.
2.12.2 Spherical interpolation
Spherical interpolation ensures that the magnitude of the interpolated vector is not comprised.
Figure 2.38 shows two unit vectors
u
and
ˆ
v
separated by an angle , which can be determined
ˆ
using
cos
−
1
=
u
ˆ
·ˆ
v
From the figure, we see that
OT
=
aTW
=
b
and TW is parallel with
v
.
ˆ
Y
W
β
v
b
w
θ
γ
β
u
T
α
a
O
X
Figure 2.38.
